This project aims to develop a series of novel approaches to phenotyping drug use and abuse. The general scheme is to develop statistical models from theory, implement them in user friendly software, and examine their statistical properties. Those models that perform sufficiently well will be applied to one or more sets of data to bring new insight into the assessment of substance use. The first goal is to extend of models for factorial invariance, which form the basis of testing for differences between groups. The primary extension will be to allow testing of invariance not merely between distinct groups, but also within groups that vary with respect to continuous variables such as age. This approach will be applied to confirmatory factor analysis, to latent class analysis, and to models that represent mixtures of both factors and latent classes, and will be able to handle binary, ordinal and continuous observed variables. The method should prove valuable in assessing whether substance abuse patterns in the population represent continuous variation in liability or whether distinct groups exist. The second goal is to extend models for regime switching in the context of growth curve and other factor mixture models. This aim is intended to provide a better model for data that involve onset and offset of substance use, and to assist in uncovering heterogeneity. Third, we will develop methods for the analysis of certain forms of partially anonymized data such as those involving randomized response. These methods will be compared for their performance at detecting relationships with predictors, sequellae and correlates of partially randomized data, including resemblance between relatives and outcomes. All model development will be designed to permit the analysis and exploitation of data collected from relatives, and will include models for data on genetic markers, for both linkage and association studies. Applied data analyses will yield substantive results, guide model development, and test for robustness. An array of cross-sectional, longitudinal, and genetically informative datasets will be assembled and analyzed.